Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what are the chances that three numbers will be drawn whose sum equals six?

1 2 3 1
2 3 1 2
3 1 2 3
1 2 3 1

• Either rolling '2 2 2' or some combination of '1 2 3' adds up to be 6. The chances of getting '2 2 2' are 5/16 (5 2s out of 16) times 4/15 (4 2s left out of 15) times 3/14 (3 2s left out of 14). This is 5/16 * 4/15 * 3/14 which equals 1/56.
  
  The chances of getting some combination of '1 2 3' is equal to 6/16 (6 1s in the list) times 5/15 (5 2s out of 15 numbers left) times 5/14 (5 3s out of 14 numbers left) times the number of different combinations of '1 2 3' which is 6. This is 6/16 * 5/15 * 5/14 * 6 which equals 15/56.
  
  1/56 + 15/56 = 16/56 or 2/7 or ~28.6%.
  
• 11 years agoHelpfull: Yes(7) No(0)
• 29% chances are there.
  detailed solution is time consuming.
• 11 years agoHelpfull: Yes(2) No(4)
• out of total possible 560 combinations, 160 combinations will give sum as 6.
  
  so % probability = 100*160/560 which is approx 29%
• 11 years agoHelpfull: Yes(2) No(4)
• 7 chances are there.
  
  Chances that drawn three numbers sum equal six :
  1,2,3 (1+2+3 = 6)
  1,3,2 (1+3+2 = 6)
  2,1,3 (2+1+3 = 6)
  2,3,1 (2+3+1 = 6)
  3,1,2 (3+1+2 = 6)
  3,2,1 (3+!+2 = 6)
  2,2,2 (2+2+2 = 6)
• 11 years agoHelpfull: Yes(1) No(4)
• 7 chances are there.
  
  Number of 1's = 6
  Number of 2's = 5
  Number of 3's = 5
  
  Chances that drawn three numbers sum equal six :
  123
  132
  213
  231
  312
  321
  
  222
• 11 years agoHelpfull: Yes(0) No(2)
• vignesh,chances means probability. work out for probability.
• 11 years agoHelpfull: Yes(0) No(5)
• six=2,2,2 or six = 1,2,3
  total number of outcomes are 16.
  chances of 2,2,2 are
  5/16*4/15*3/14=1/56(no repitition)
  chances of 1,2,3 are
  6/16*5/15*5/14*6 = 15/56
  (multiply by 6, because 1,2,3 can be arranged in 6 ways.)
  (1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1).
  total possible outcomes = 1/56 + 15/56=16/56
  2/7.
• 11 years agoHelpfull: Yes(0) No(0)
• well if the word random also means at once.. then we c t hat the probability is
  15/56
  which is solved by total events = (6C1 * 5C1 * 5C1 )/16C3
• 11 years agoHelpfull: Yes(0) No(0)